A reliable extraction of time-dependent and momentum-resolved QFI \(f_\mathrm {Q}(q, t)\)  allows us to witness the entanglement depth of the driven EHM. As originally investigated in pure spin systems [1]}, [2]}, [3]}, the QFI informs about the presence of an entangled many-body state if its value exceeds a minimum value derived from the quantum Cramer-Rao bound. To witness entanglement dynamics in the spin sector, we determine a quantum bound suited to diagnose multipartite entanglement after obtaining the time-dependent QFI. Since the doped fermionic model has a local magnetic moment \(\langle m_z^2\rangle <1\) , we normalize the QFI bound by reducing the total spin \(S\)  by the doping concentration. This implies that, for a \(k\) -producible state, the QFI obtained by RIXS spectrum is bounded by
\({f_\mathrm {Q}(q, t)} \le 4kn^2S^2\,\) 
